Uniqueness, symmetry and nodal sets for a Ginzburg–Landau type problem in an infinite strip

par Amandine Aftalion (LMO (Orsay))

jeudi 1 oct. 2026, 11:15 → 12:15 Europe/Paris

Amphi Schwartz

The Ginzburg-Landau energy is studied in a specific geometry: an infinite strip with Neumann boundary conditions and under symmetry properties related to very experiments in Bose Einstein condensates.  We show that there is a unique minimizer when the width of the strip is below an explicit threshold. This solution is in fact a one dimensional soliton. Above the threshold, the soliton becomes unstable and we prove the minimizer vanishes at a single point, with a solitonic behaviour at infinity, therefore very different from a classical vortex. The same solutions are recovered as mountain pass critical points in a larger symmetry class. We also show that there exist stationary solutions to the Gross-Pitaevskii equation with k vortices on a transverse line, which bifurcate from the soliton solution as the width of the strip is increased.

Joint work with L. Nguyen, and with E. Sandier and Ph. Gravejat.